Free vibration analysis of rotating nonlinearly elastic structures with symmetry: An efficient group-equivariance approach (Q1362194)

We show that the use of group-theoretic ideas can greatly simplify the procedure for finding both linear vibration modes and frequencies and locating solution branches for nonlinear vibration problems. These methods can be employed in both analytic and numerical settings, and they lead to dramatic increases in solving efficiency via block diagonalization. For the class of problems studied here (in which gyroscopic effects are present), we demonstrate that the original structural symmetry group can be employed to analyze the dynamics of the system despite the loss of reflection symmetry. In addition, we explain how ideas from bifurcation theory can be included with symmetry analysis to prove the existence of solution branches for nonlinear vibration problems.